Problem: What is the surface area of a cylinder with base radius $3$ and height $9$ ? 3 9
Answer: The areas of the top and the base are simply the area of a circle: $\pi r^2 = \pi \cdot 3^2 = 9 \pi$ The lateral surface area is the same as the area of a rectangle with height $9$ and width equal to the circumference of the base. That circumference is $2 \pi r = 2\pi \cdot 3 = 6\pi$ Thus, the lateral surface area is $wh = 6 \pi \cdot 9 = 54 \pi$ The total surface area is $9 \pi + 9 \pi + 54 \pi = 72\pi$.